Photo-Curing Kinetics of 3D-Printing Photo-Inks Based on Urethane-Acrylates

In this study, photo-curing kinetics for urethane-acrylate-based photo-inks for 3D printing were evaluated using a photo-differential scanning calorimetry analysis. Initially, the photopolymerization kinetics of di- and monofunctional monomers were separately studied at different temperatures (5–85 °C). Later, the photo-curing kinetics and mechanical properties of photo-inks based on different monomer mixtures (40/60–20/80) were evaluated. The results showed that urethane-dimethacrylate (UrDMA) and urethane-acrylate (UrA) had no light absorption in the region of 280–700 nm, making them a proper crosslinker and a reactive diluent, respectively, for the formulation of 3D-printing photo-inks. The kinetics investigations showed a temperature dependency for the photo-curing of UrDMA, where a higher photopolymerization rate (Rp,max: from 5.25 × 10−2 to 8.42 × 10−2 1/s) and double-bound conversion (DBCtotal: from 63.8% to 92.2%) were observed at elevated temperatures (5–85 °C), while the photo-curing of UrA was independent of the temperature (25–85 °C). Enhancing the UrA content from 60% to 80% in the UrDMA/UrA mixtures initially increased and later decreased the photopolymerization rate and conversion, where the mixtures of 30/70 and 25/75 presented the highest values. Meanwhile, increasing the UrA content led to lower glass transition temperatures (Tg) and mechanical strength for the photo-cured samples, where the mixture of 30/70 presented the highest maximum elongation (εmax: 73%).

The main research trend for light-based, 3D-printing technologies is focused on the development of advanced photo-ink formulations and innovative processes to obtain high-performance constructs for cutting-edge applications [1,15]. Meanwhile, the fundamental investigation of the photopolymerization kinetics of photo-inks has been less reported [10,[16][17][18]. To better understand the characteristics of photo-inks and, consequently, to improve the quality and performance of 3D-printed constructs, studying photo-curing kinetics is essential. Recently, Jiang et al. [17] reported that higher UV intensity improved the photo-curing rate (R p ) and the double-bound conversion (DBC) of a photo-ink based on 1,6-hexamethylene diacrylate, while longer exposure time partially enhanced the DBC. Deng et al. [10] reported that enhancing the concentration of the photoinitiator improved the R p and DBC values for photo-ink formulations based on urethane-acrylates. According to Kim et al. [18], higher temperature led to higher R p , DBC, and glass transition temperature (T g ) values for a commercial UV-curable, 3D-printing acrylic resin (VeroWhitePlus RGD 835, Stratasys Ltd., Minneapolis, MN, USA). Bachmann et al. [16] studied the photo-curing kinetics of three commercial photo-inks for DLS 3D printing under different wavelengths, light intensities, temperatures, relative humidities, and atmospheric oxygen concentrations. One of their observations was the improvement of R p by decreasing the atmospheric oxygen concentration, which is the reason behind a shorter printing time under an inert atmosphere.

Instruments
UV-Vis spectroscopy of the monomers and photoinitiator in an acetonitrile solution (0.8 g/L) was performed using a PerkinElmer instrument (Lambda 950, Norwalk, CT, USA) operating in the range of 200-700 cm −1 . Acetonitrile was used as a blank solution.
A DSC from Netzsch (DSC 204 F1 Phoenix, Mannheim, Germany) equipped with a UV-curing spot system (OmniCure®S2000, Lumen Dynamics, Toronto, ON, Canada) was employed to study the photo-curing of the samples. The experiments were conducted in an isothermal mode (5, 25, 45, 65, or 85 • C) with a UV intensity of 1 W/m 2 under N 2 atmosphere. The UV intensity was measured with a radiometer (R2000 Radiometer, Lumen Dynamics, Toronto, ON, Canada). The samples were weighted in uncovered aluminum pans in darkness and analyzed immediately. An empty, uncovered aluminum pan was employed as a reference. The irradiation step was prolonged up to 3 min for the full photocuring of the samples and reached a plateau region, which was employed as a baseline for the peak integrations. The T g of the photo-cured samples was determined using DSC measurements in the temperature range of −50 to 200 • C with the heating rate of 10 • C/min under N 2 atmosphere. The T g values were extracted from the middle point of the baseline change in the first heating cycle.
The tensile properties of the photo-cured specimens were measured with a Zwick/Roell machine (model Z020, Ulm, Germany) equipped with a load cell of 100 N at room temperature. Photo-cured samples with a thickness of 300-500 µm were cut into 8 × 2 cm 2 pieces and analyzed with a clamping length of 34 mm and a crosshead speed of 17 mm/min. The reported values were the averages of at least three specimens for each sample.

Methods
The R p (1/s) and DBC (%) values as a function of time were calculated from the photo-DSC data using Equations (1)-(3) [7]: where ∆H theor (J/g) is the theoretical total heat released during the complete polymerization of the monomers within the sample, f is the mass fraction of each monomer within the sample, n is the number of double bonds in each monomer, ∆H 0 (J/mol) is the standard heat of polymerization for either methacrylate (54.8 kJ/mol [19,20]) or acrylate (86.2 kJ/mol [20,21]), M w (g/mol) is the molecular weight of each monomer, dH p /dt (J/s·g or W/g) is the normalized heat flow per second, and ∆H p (J/g) is the heat generated from the start of photo-curing up to a certain time that is obtained from the integration of the thermograms.
To prepare tensile test specimens, formulations based on UrDMA/UrA mixtures (40/60-20/80) containing TPOL (1 wt.%) were cast with a thickness of 700 µm on a PET substrate using an adjustable applicator and cured under a UV lamp (145 mW/m 2 ) for 60 s. After washing in isopropanol, the backs of the films were post-cured for 60 s.
where ΔHtheor (J/g) is the theoretical total heat released during the c of the monomers within the sample, f is the mass fraction of ea sample, n is the number of double bonds in each monomer, ΔH heat of polymerization for either methacrylate (54.8 kJ/mol [19,20 [20,21]), Mw (g/mol) is the molecular weight of each monomer, d normalized heat flow per second, and ΔHp (J/g) is the heat gen photo-curing up to a certain time that is obtained from the integra To prepare tensile test specimens, formulations based on (40/60-20/80) containing TPOL (1 wt.%) were cast with a thickn substrate using an adjustable applicator and cured under a UV l s. After washing in isopropanol, the backs of the films were post

UV-vis Absorption
Under a light, photoinitiator molecules absorb energy, con and generate free radicals to initiate the photopolymerization of

UV-vis Absorption
Under a light, photoinitiator molecules absorb energy, convert to an excited state, and generate free radicals to initiate the photopolymerization of monomers. Before studying the photopolymerization kinetics of monomers, their UV-vis spectra in an acetonitrile solution were recorded ( Figure 1). Both monomers (UrDMA and UrA) were transparent in the region of 280-700 nm, which is ideal for the photo-curing process since the whole irradiated light is accessible to the photoinitiator molecules. Meanwhile, TPOL showed absorption in the range of 200-420 nm, with two maximums at 273 and 371 nm. The absorption at 371 nm makes TPOL active for commercial DLP 3D printers and post-curing units, which mainly function at 365, 385, or 405 nm.
Polymers 2022, 14, x FOR PEER REVIEW 4 ying the photopolymerization kinetics of monomers, their UV-vis spectra in an ac trile solution were recorded ( Figure 1). Both monomers (UrDMA and UrA) were parent in the region of 280-700 nm, which is ideal for the photo-curing process sin whole irradiated light is accessible to the photoinitiator molecules. Meanwhile, T showed absorption in the range of 200-420 nm, with two maximums at 273 and 37 The absorption at 371 nm makes TPOL active for commercial DLP 3D printers and curing units, which mainly function at 365, 385, or 405 nm.

Photo-Curing
The most common type of photopolymerization for 3D-printing applicatio through the free-radical mechanism, which involves three main steps: (1) initiatio propagation, and (3) termination [15]. In the initiation step, the photoinitiator mole are disintegrated under light irradiation and produce reactive radical fragments. I propagation step, these radical species react with the double bonds (C=C) of mon molecules to generate growing polymer chains. The growth of these polymer chains tinues simultaneously with the addition of further monomers and the formation of m radicals. In the termination step, the growing polymer chains are deactivated thr combination, radical disproportionation, or chain transfer reactions [15].
Photo-DSC analyses have been widely utilized to evaluate the photo-activity o printing photo-inks [7,16,17]. Primarily, the photopolymerization kinetics of difunc UrDMA and monofunctional UrA were studied separately in the isothermal mode a ferent temperatures, i.e., at 5, 25, 45, 65, or 85 °C ( Figure 3b), whic known as the auto-acceleration and auto-deceleration phenomena, respectively. Th servation was due to the gradual increase in viscosity with conversion and, consequ the decrease in molecular mobility of the monomers and macroradicals within the p curing mixture over time [28,29]. Initially, at a low viscosity, the Rp of the liquid mono was constant and dependent on the double-bond activity (chemistry-controlled). La medium viscosity, the coupling of macroradicals in the photo-curing mixture for ter tion was diffusion-limited when the monomers were still mobile for propagation thus, the Rp increased (auto-acceleration). Finally, at a high viscosity, when the photo ing mixture was transforming into a rubbery, glassy network (gel point), the diffus monomers to reach the macroradicals was significantly restricted, and therefore, t decreased (auto-deceleration) [28,29]. For both UrDMA and UrA, the DBC sharp creased over the first 20-30 s of the photo-curing process and remained constant af s (Figures 2c and 3c). The total double-bound conversion (DBCtotal) values obtained the total generated photo-curing heat (ΔHp,total) were less than unity due to the gelat

Photo-Curing
The most common type of photopolymerization for 3D-printing applications is through the free-radical mechanism, which involves three main steps: (1) initiation, (2) propagation, and (3) termination [15]. In the initiation step, the photoinitiator molecules are disintegrated under light irradiation and produce reactive radical fragments. In the propagation step, these radical species react with the double bonds (C=C) of monomer molecules to generate growing polymer chains. The growth of these polymer chains continues simultaneously with the addition of further monomers and the formation of macroradicals. In the termination step, the growing polymer chains are deactivated through combination, radical disproportionation, or chain transfer reactions [15].
Photo-DSC analyses have been widely utilized to evaluate the photo-activity of 3Dprinting photo-inks [7,16,17]. Primarily, the photopolymerization kinetics of difunctional UrDMA and monofunctional UrA were studied separately in the isothermal mode at different temperatures, i.e., at 5, 25, 45, 65, or 85 • C (Figures 2a and 3a). The R p and DBC values as a function of irradiation time were calculated from the photo-DSC data according to Equations (1)-(3) (Figures 2b-d and 3b-d). For both UrDMA and UrA, the R p value, an overall value of the propagation and termination rates, initially increased and later decreased during the photo-curing process (Figures 2b and 3b), which are known as the auto-acceleration and auto-deceleration phenomena, respectively. This observation was due to the gradual increase in viscosity with conversion and, consequently, the decrease in molecular mobility of the monomers and macroradicals within the photo-curing mixture over time [28,29]. Initially, at a low viscosity, the R p of the liquid monomers was constant and dependent on the double-bond activity (chemistry-controlled). Later, at medium viscosity, the coupling of macroradicals in the photo-curing mixture for termination was diffusion-limited when the monomers were still mobile for propagation, and thus, the R p increased (auto-acceleration). Finally, at a high viscosity, when the photo-curing mixture was transforming into a rubbery, glassy network (gel point), the diffusion of monomers to reach the macroradicals was significantly restricted, and therefore, the R p decreased (autodeceleration) [28,29]. For both UrDMA and UrA, the DBC sharply increased over the first 20-30 s of the photo-curing process and remained constant after 40 s (Figures 2c and 3c). The total double-bound conversion (DBC total ) values obtained from the total generated photo-curing heat (∆H p,total ) were less than unity due to the gelation or vitrification phenomenon [28,29], which meant that all the double bonds did not react in the course of the photo-curing process (Tables 1 and 2). to 122 °C, which was expected according to the DBCtotal trend, where more conversion for difunctional UrDMA resulted in networks with higher crosslinking densities, lower polymer chain flexibility, and consequently, higher Tg values. It is worth mentioning that, for all the photo-cured samples, the Tg values were higher than the Tp, which meant that the conversion was restricted due to the transformation of the liquid monomer to a glassy network with insufficient molecular mobility [31].     For monofunctional UrA, the Rp,max remained constant in the range of 5.08 × 10 −2 -5.47 × 10 −2 1/s by increasing the Tp from 5 to 85 °C (Table 2). In the Tp range of 25-85 °C, the tGP, DBCGP, and DBCtotal remained constant in the ranges of 5.2-5.7 s, 16.5-18.5%, and 83.3-83.8%, respectively. These phenomena meant that raising the temperature did not affect the photo-activity and conversion of UrA, which is in contrast with previous results about 2-hydroxyethyl acrylate (HEA) [11], undecyl amide N-ethyl acrylate [12], and 2-carboxyethyl acrylate [33], where the Rp,max has decreased with increasing Tp from 25 °C to 90 °C as a result of the dissociation of the intermolecular hydrogen bonding and disappearance of the pre-association of monomers. At 5°C, UrA displayed a shorter tGP (4.4 s) and lower DBCGP (11.9%) and DBCtotal (78.7%) values, which was attributed to the crystallization of UrA molecules with a melting point (Tm) of 5 °C, leading to lower molecular mobility within the photo-curing mixture. This observation is in agreement with a previous report on crystalizable monomers [7].
In the Tp range of 25-85 °C, t50%, t90%, and t95% were shortened by increasing the temperature, which meant faster photo-curing processes at higher temperatures. The Tg of the photo-cured samples remained constant at −11 °C in the Tp range of 5-65 °C and then partially increased to −8 °C at a Tp of 85 °C, which was expected due to almost the same DBCtotal values. For all the photo-cured samples, the Tg values were lower than the Tp, meaning the photo-curing mixture transformed from a low-viscosity liquid monomer into a rubbery network with flexible polymer chains. It is worth mentioning that, although the photo-cured monofunctional UrA was supposed to be a thermoplastic, the DSC analyses up to 200 °C did not show any exothermic melting peak.    For difunctional UrDMA, the maximum photo-curing rate (R p,max ) gradually increased from 5.25 × 10 −2 to 8.42 × 10 −2 1/s by raising the photo-curing temperature (T p ) from 5 to 85 • C (Table 1). Meanwhile, the gel-point time (t GP ), the time to reach R p,max , decreased from 7.0 to 3.3 s, and the gel-point conversion (DBC GP ), the conversion at R p,max , increased from 10.9% to 12.3%. These observations showed higher photo-activity leading to faster photopolymerization for UrDMA at elevated temperatures, which is in agreement with previous reports on multifunctional monomers [28,[30][31][32]. The increase in R p,max values by raising the temperature can also be explained according to Arrhenius' law (Equation (4)) [31]: (4) where k is the overall photopolymerization rate constant equal to the propagation rate constant (k p ) at low conversions, E a is the activation energy, A is the frequency factor, R is the ideal gas constant, and T is the absolute temperature. According to Arrhenius' law, a rise in temperature results in an increase in k and, consequently, R p,max . On the other hand, the DBC total of UrDMA was improved from 63.8% to 92.2% (Table 1) due to lower viscosity and higher molecular mobility within the photo-curing mixture at higher temperatures, which is in agreement with previous reports [28,[30][31][32]. Meanwhile, the times to reach 50%, 90%, and 95% of DBC total (t 50% , t 90% , and t 95% , respectively) were shortened, which meant faster photo-curing processes at elevated temperatures. The T g of the photo-cured samples obtained from DSC measurements was improved from 63 to 122 • C, which was expected according to the DBC total trend, where more conversion for difunctional UrDMA resulted in networks with higher crosslinking densities, lower polymer chain flexibility, and consequently, higher T g values. It is worth mentioning that, for all the photo-cured samples, the T g values were higher than the T p , which meant that the conversion was restricted due to the transformation of the liquid monomer to a glassy network with insufficient molecular mobility [31].
For monofunctional UrA, the R p,max remained constant in the range of 5.08 × 10 −2 -5.47 × 10 −2 1/s by increasing the T p from 5 to 85 • C ( Table 2). In the T p range of 25-85 • C, the t GP , DBC GP , and DBC total remained constant in the ranges of 5.2-5.7 s, 16.5-18.5%, and 83.3-83.8%, respectively. These phenomena meant that raising the temperature did not affect the photo-activity and conversion of UrA, which is in contrast with previous results about 2-hydroxyethyl acrylate (HEA) [11], undecyl amide N-ethyl acrylate [12], and 2-carboxyethyl acrylate [33], where the R p,max has decreased with increasing T p from 25 • C to 90 • C as a result of the dissociation of the intermolecular hydrogen bonding and disappearance of the pre-association of monomers. At 5 • C, UrA displayed a shorter t GP (4.4 s) and lower DBC GP (11.9%) and DBC total (78.7%) values, which was attributed to the crystallization of UrA molecules with a melting point (T m ) of 5 • C, leading to lower molecular mobility within the photo-curing mixture. This observation is in agreement with a previous report on crystalizable monomers [7].
In the T p range of 25-85 • C, t 50% , t 90% , and t 95% were shortened by increasing the temperature, which meant faster photo-curing processes at higher temperatures. The T g of the photo-cured samples remained constant at −11 • C in the T p range of 5-65 • C and then partially increased to −8 • C at a T p of 85 • C, which was expected due to almost the same DBC total values. For all the photo-cured samples, the T g values were lower than the T p , meaning the photo-curing mixture transformed from a low-viscosity liquid monomer into a rubbery network with flexible polymer chains. It is worth mentioning that, although the photo-cured monofunctional UrA was supposed to be a thermoplastic, the DSC analyses up to 200 • C did not show any exothermic melting peak.
Later, the photopolymerization kinetics of different UrDMA/UrA mixtures (40/60-20/80) as bases for photo-inks were evaluated in isothermal mode at 25 • C ( Figure 4 and Table 3). The R p,max and DBC total for the UrDMA/UrA mixtures were higher (7.35 × 10 −2 -9.50 × 10 −2 1/s and 90-92%, respectively) compared with pure UrDMA and UrA at 25 • C, while t 50% , t 90% , and t 95% were shorter. These observations showed higher photo-activity, leading to faster photopolymerization and higher conversion for the UrDMA/UrA mixtures.    By enhancing the content of the monofunctional reactive diluent (UrA) from 60% to 80% in the UrDMA/UrA mixtures, the R p,max , t GP , DBC GP , DBC total initially increased and then decreased, where the mixtures of 30/70 and 25/75 presented the highest values (Table 3). Meanwhile, t 50% , t 90% , and t 95% initially decreased and then increased. Since UrA has a lower viscosity (η = 35 mPa·s) than UrDMA (η = 9500 mPa·s), increasing the UrA content led to photo-curing mixtures with lower viscosity. At the same time, it resulted in lower average double-bound functionality within the photo-curing mixture and, consequently, later gelation. Both phenomena enhanced the molecular mobility within the photo-curing mixture, which explained the initial increasing trend for the R p,max , t GP , DBC GP , DBC total values, as well as the decreasing trend for the t 50% , t 90% , and t 95% values. Therefore, faster photopolymerization and higher conversion were observed for the mixtures of 30/70 and 25/75. The later decreasing trend for the R p,max , t GP , DBC GP , DBC total values and the increasing trend for the t 50% , t 90% , and t 95% values, especially for the mixture of 20/80, could be attributed to the higher deactivation of macroradicals through the combination of macroradicals and, thus, the limited auto-acceleration at a very low viscosity.
The T g of the photo-cured samples decreased from 23 to −11 • C by increasing the UrA content from 60% to 80%, which was expected due to the reduction in the average double-bound functionality, the crosslinking density of the polymeric network, and thus, the polymer chain flexibility. For all the photo-cured samples, the T g values were lower than 25 • C, meaning the photo-curing mixture transformed from a viscous liquid monomer into a rubbery network with flexible polymer chains.

Mechanical Properties
Enhancing the content of the monofunctional reactive diluent in photo-inks, which decreased the average double-bound functionality, could influence the mechanical properties of 3D-printed objects. The mechanical properties of the photo-cured samples were investigated with tensile tests ( Figure 5). The results presented the typical stress-strain curves of a thermoset polymer (Figure 5a). Enhancing the UrA content from 60% to 80% led to a decrease in the tensile module (E) from 248.8 to 5.4 MPa (Figure 5b) and tensile strength (σ max ) from 13.6 to 1.9 MPa (Figure 5c), which was expected due to the reduction in the crosslinking density of the polymeric network as a result of the fall in the average double-bound functionality within corresponding photo-curing mixtures. Meanwhile, the maximum elongation (ε max ) initially increased from 41% to 73% (for the mixture of 30/70) and then decreased to 50% (Figure 5d). These observations are in agreement with a previous report about photo-cured elastomers based on mono-and difunctional urethane-acrylates [10].

Conclusions
UrDMA and UrA with no light absorption in the region of 280-700 nm were pre sented as a proper crosslinker and a reactive diluent, respectively, for the formulation o 3D-printing photo-inks. Kinetics investigations showed a temperature dependency for th photo-curing of UrDMA, where higher photopolymerization rates, conversion, and T were observed at elevated temperatures, while the photo-curing of UrA was independen of temperature (25-85 °C). Enhancing the UrA content from 60% to 80% in th UrDMA/UrA mixtures initially increased and later decreased the photopolymerizatio rate and conversion, where the mixtures of 30/70 and 25/75 presented the highest value Meanwhile, increasing the UrA content led to lower Tg, E, and σmax values for the photo cured samples, where the mixture of 30/70 presented the highest εmax value. For futur investigations, studying the effects of other parameters, such as photoinitiator type an concentration, not only on photo-curing kinetics but also on the 3D printability of photo inks may be interesting. Employing other instruments, such as online FTIR or a rheomete may be helpful to better understand the chemical changes during the photo-curing pro cess.

Conclusions
UrDMA and UrA with no light absorption in the region of 280-700 nm were presented as a proper crosslinker and a reactive diluent, respectively, for the formulation of 3D-printing photo-inks. Kinetics investigations showed a temperature dependency for the photo-curing of UrDMA, where higher photopolymerization rates, conversion, and T g were observed at elevated temperatures, while the photo-curing of UrA was independent of temperature (25-85 • C). Enhancing the UrA content from 60% to 80% in the UrDMA/UrA mixtures initially increased and later decreased the photopolymerization rate and conversion, where the mixtures of 30/70 and 25/75 presented the highest values. Meanwhile, increasing the UrA content led to lower T g , E, and σ max values for the photo-cured samples, where the mixture of 30/70 presented the highest ε max value. For future investigations, studying the effects of other parameters, such as photoinitiator type and concentration, not only on photo-curing kinetics but also on the 3D printability of photo-inks may be interesting. Employing other instruments, such as online FTIR or a rheometer, may be helpful to better understand the chemical changes during the photo-curing process.